Can you please help me with this..

see explanation

Step-by-step explanation:

A difference of cubes factors in general as

a³ - b³ = (a - b)(a² + ab + b²)

Thus

(n + 1)³ - n³ → with a = n + 1 and b = n

= (n + 1 - n)((n + 1)² + n(n + 1) + n²) ← simplifying

= 1 (n² + 2n + 1 + n² + n + n²)

= 3n² + 3n + 1 ← factor out 3n from the first 2 terms

= 3n(n + 1) + 1

= 6m + 1 ( since n or n + 1 is even )

= odd

6m is always even for m ∈ Z ( the set of integers )

Thus 6m + 1 is always odd

Example

m = 1 → 6 + 1 = 7

m = 2 → 12 + 1 = 13

m = 3 → 18 + 1 = 19

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol

there is no graph so i cant sorry

step-by-step explanation: